Yes I would scrap them to be replaced by things like critical illness cover, early retirement etc.
You can then opt if you want them (to what level), if you want to risk it with nothing (say own a business that will continue without much input) or employers can provide it on a group policy as an employment benefit.
It could be a legal requirement for companies to provide life long cover for illness in kids born under the policy, where that event occurs up to age 18, at which age they purchase their own policy.
With it being a private scheme the money can be invested unlike tax (I.e pension schemes) to provide the return to fund the system plus profit. The current system is just a cost to the government without a long term way of funding it.
I can't think of a way of funding education without it being atleast partly through tax but would be open to options. I also wouldn't oppose private healthcare on a larger scale, but considering the pure size of the NHS dismantling it to replace with a private system is a pipe dream even for the Tory's. I think the closest they will get in the next few decades is making it into a two tier system.
If they introduce 1% deposit mortgages the 10 would be a sufficient deposit for anyone!